Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;
public class Main{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }
    static int L,R,top,bottom;
    static int cnt,edge;
    public static void solve(InputReader sc, PrintWriter pw) {
        // int t=sc.nextInt();
        int t=1;
        u:while(t-->0){
            int a,b,k;
            a=sc.nextInt();
            b=sc.nextInt();
            k=sc.nextInt();
            char[] chrr=new char[a+b];
            for(int i=0;i<b;i++)
                chrr[i]='1';
            for(int i=b;i<a+b;i++)
                chrr[i]='0';
            String s;
            if(a==0||b==1){
                if(k>0)
                    pw.println("No");
                else{
                    pw.println("Yes");
                    s=new String(chrr);
                    pw.println(s);
                    pw.println(s);
                }
                continue;
            }
            if(k>a+b-2){
                pw.println("No");
                continue;
            }
            pw.println("Yes");
            s=new String(chrr);
            pw.println(s);
            chrr[b-1-(Math.max(k,a)-a)]='0';
            chrr[b-1+Math.min(k,a)]='1';
            s=new String(chrr);
            pw.println(s);
        }
    }
    public static long find_val(long n){
        char[] chrr=(""+n).toCharArray();
        Arrays.sort(chrr);
        return Long.parseLong(new StringBuilder(new String(chrr)).reverse().toString())-Long.parseLong(new String(chrr));
    }
    public static int ask(int l, int r, InputReader sc){
        System.out.println("? "+l+" "+r);
        System.out.flush();
        return sc.nextInt();
    }
    public static void sort(long []arr){
        ArrayList<Long> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int num(int n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    static class Pair{
        int a, b;
        Pair(int a,int b){
            this.a=a;
            this.b=b;
        }
     //*
    }
    /*/
        public int compareTo(Pair p){
            return (b-p.b);
        }
        public int hashCode(){
            int hashcode = (a+" "+b).hashCode();
            return hashcode;
        }
        public boolean equals(Object obj){
            if (obj instanceof Pair) {
                Pair p = (Pair) obj;
                return (p.a==this.a && p.b == this.b);
            }
            return false;
        }
    }
    //*/
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
    static int gcd(int a, int b) { 
        if (b == 0) 
            return a; 
        return a>b?gcd(b, a % b):gcd(a, b % a);  
    } 
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static void feedArr(long []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr,InputReader sc){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}